Multiply Radical Expressions

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What is a radical expression?

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A radical expression is an expression that includes a root, such as a square root, cube root, etc. For example, @@ ext{radical expression} = ext{ } oot{n}{x}@@.

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How do you simplify a radical expression?

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To simplify a radical expression, factor the number under the radical into its prime factors and look for perfect squares (or cubes, etc.) to simplify.

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What is the product of two square roots?

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The product of two square roots can be simplified using the property: @@ ext{If } a ext{ and } b ext{ are non-negative, then } oot{2}{a} imes oot{2}{b} = oot{2}{ab}@@.

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What is the distributive property in multiplication?

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How do you multiply a radical expression by a whole number?

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To multiply a radical expression by a whole number, simply multiply the whole number by the coefficient of the radical. For example, @@3 oot{2}{5} = 3 oot{2}{5}@@.

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What is the result of @@ oot{2}{a} imes oot{2}{a}@@?

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How do you combine like terms in radical expressions?

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Like terms in radical expressions can be combined if they have the same radical part. For example, @@2 oot{2}{3} + 3 oot{2}{3} = 5 oot{2}{3}@@.

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What is the simplified form of @@ oot{12}@@?

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What does it mean to rationalize the denominator?

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Rationalizing the denominator means to eliminate any radicals in the denominator of a fraction. This is done by multiplying the numerator and denominator by a suitable radical.

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What is the result of @@ oot{5} imes oot{5}@@?

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